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In this paper, we design a segment training based individual channel estimation (STICE) scheme in the classical three-node it amplify-and-forward (AF) one-way relay network (OWRN). The linear minimum mean-square-error (LMMSE) channel estimator is used to obtain a good initialization, and an iterative maximum a posteriori (MAP) channel estimator is developed to improve the estimation accuracy. We then investigate the underlying power allocation at the relay node both to minimize the mean-square-error (MSE) of the individual channel estimation and to maximize the average effective signal-to-noise ratio (AESNR) of the data detection. The closed-form Bayesian Cramér-Rao Bound (CRB) is also derived to evaluate the proposed algorithm. Finally, numerical results are provided to corroborate the proposed studies.